Patricia is building the community dog park. She plans to build the dog park right beside the city park so she can use one side of the existing fence. Her budget allows her to purchase 340 feet of fencing. In order to make the area of the dog park as large as possible, determine the dimensions of the dog park if one side of the fence is attached to the city park’s fence.

85 feet by 170 feet

Step-by-step explanation:

This one relies on Calculus.

so you have 340   feet.

Let  x = width,   y = length of rectangle

one side of this rectangle will not use the new fence material

so  2x + y = 340 feet.

Area = x*y

We want to maximize  Area

Area  A = x*y = x*(340 - 2x)

Take the derivative of A  w.r.t.  x

dA/dx =  340 - 4x

set it to 0

340 - 4x = 0

4x = 340

x = 85 feet

and y = 340 - 2x = 340 - 2*85 = 340 - 170 = 170 feet

step-by-step explanation: